Uhh hello!
I've heard a lot about worshiping different godexes (gods) but am not sure exactly how it works?
For example, someone worships Aphrodite, what does that exactly consist of?
I'd like to have a shrine and worship Bast, but i'm not sure how I would?
Please reply or mail me with any information, or correct me if I am wrong about anything?

If you want to dedicate your time to two different God/esses from two different pantheons, make sure you know what you're doing. Some people are touchy on the subject of mixing pantheons. Some don't like it, others, like me, don't mind. I'm actually a follower of Aphrodite. It's been a long and hard journey, but I think it's been worth it. She not only teaches you to love others, but to love yourself. If you also want to follow Bastet, that's fine, just space it out. If you'd like to build altars to two different deities, just be careful that you don't use the same candle for two deities, or the same space for both at the same time.

The thing with following Greeks is, they think that they are the highest of them all. So you've just gotta be a little wary of that.

Worship is different for everyone, and is influenced by whatever "path" you choose be it Wiccan, Druid, Heathen, etc.

I know almost nothing about the Egyptian pantheon, but since you've chosen Bast as a patron goddess I assume that you do. To make a shrine, set up a space that is relatively out of the way so that no one will accidentally bump into it and break whatever you choose to put on it. In your shrine space you could have a statue of Bast and various other things representative of Bast as a way to start out. As for how you would go about your worship of Bast, that should be unique to you. Research Bast and worship her however it feels right to you. When working with a deity, they will reveal to you how they like things.